To hear Michael Cohen’s spokesman and lawyer Lanny Davis tell it, his client’s bombshell admission in court Tuesday that President Donald Trump directed him to make a $130,000 hush-money payment that violated campaign finance law unambiguously implicates Trump in a crime.

Not so fast, many lawyers say.

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Cohen’s admission that he violated campaign finance law while acting at Trump’s direction is far from rock-solid proof that the president is also guilty, even if Cohen is being entirely truthful, these lawyers said.

Cohen said in court on Tuesday that he acted at Trump’s “direction” and violated federal election laws by arranging the payout to Stormy Daniels, an adult-film actress, in the days before the 2016 election to keep her silent about what she said was an affair with Trump a decade earlier.

But a very high legal standard that is applied in criminal cases involving alleged campaign finance violations means Trump might not be guilty even if his lawyer is.

“Under the law, it’s quite easy for two people involved in the same act to have different criminal consequences,” said Andy Grewal, a University of Iowa law professor.

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That distinction is particularly critical in campaign finance cases because the law limits criminal prosecutions on those charges to instances where someone “knowingly and willfully” defied legal requirements.

In his plea Tuesday in U.S. District Court in Manhattan, Cohen admitted that he was intending to benefit Trump’s presidential bid when he arranged the payment to Daniels and another payment of $150,000 to a former Playboy playmate, Karen McDougal. Daniels claimed a one-time sexual encounter with Trump, who was married at the time. McDougal said she had sex with Trump dozens of times over a 10-month period.

During a morning TV blitz on Wednesday, Davis said his client’s statement meant that Trump also broke the law.

Cohen “said under oath the most damaging definitive information yesterday, that the president of the United States committed a crime and covered it up,” Davis told NBC.

“The agreement in the Southern District [of New York] was about a crime that Michael Cohen admitted to and said that the president of the United States directed and coordinated that crime, making him complicit and equally culpable,” Davis added on CNN.

But as a lawyer, Cohen could be assumed to have some familiarity with federal election law. Prosecutors may well have proof in emails or other documents that he regularly discussed compliance with such statutes.

Proving that Trump knew at the time that the payouts were intended to influence the presidential race, and that he knew they were illegal, could be much harder. Perhaps such records exist, or maybe Cohen is prepared to say that he told Trump the way they were handling it was illegal, but the lawyer never said that in court on Tuesday.

“In order to prove criminal intent, you have to point to evidence that the actors knew or had reason to know what they were doing was illegal,” said Baran, the GOP campaign finance lawyer.

He said that some issues in campaign finance law were relatively straightforward, like the dollar limit on contributions or that a person can’t lie in reports filed with the Federal Election Commission. But questions of how the law treats payments that have both personal and electoral benefits prompt a lot of disputes even among attorneys who are experts in the field, he said.

“If that many people don’t know what the law means, then it can be very hard to convict anybody of violating a campaign finance law,” Baran said.

Trump seemed to adopt part of that strategy on Wednesday by asserting that the payments Cohen admitted involvement in were not criminal, echoing earlier claims by Rudy Giuliani, the president’s personal lawyer, that payments to the women were personal expenses that had nothing to do with the campaign.

“They didn’t come out of the campaign,” Trump told Fox News. “In fact, my first question, when I heard about it, [was] ‘Did they come out of the campaign, because that could be a little dicey?’ — because that could be a little dicey. It is not even a campaign violation.”

The president later added on Twitter: “Michael Cohen plead [sic] guilty to two counts of campaign finance violations that are not a crime.”

However, the president also appeared to dispute Cohen’s claim that he acted at Trump’s direction, notwithstanding an audio recording made public last month in which Trump and Cohen seem to discuss the mechanics of the McDougal payments.

In the Fox interview Wednesday, Trump appeared to say he didn’t know about the payments to women as they were being made: “Later on, I knew. … Later on.”

Davis did not respond to multiple requests for comment on Wednesday.

If prosecutors are seeking to establish whether Trump had criminal intent, they’ll scramble to find proof that he understood that money paid to influence an election had to be reported and couldn’t lawfully be paid through a corporation in coordination with a candidate or campaign. They might even need proof that Trump knew expenses arguably of a personal nature could be considered campaign donations.

The most famous such case in recent memory was the prosecution of former Sen. John Edwards (D-N.C.) in connection with nearly $1 million in expenses that some of his top campaign donors paid to help keep quiet his affair with Rielle Hunter, a videographer who worked on Edwards’ presidential bid. Edwards was indicted over the payments in 2011 and went to trial on the charges in Greensboro the following year.

Trump indicated on Twitter and in a TV interview that he was following the Edwards case, which involved many of the same issues posed by the payments Cohen arranged.

“I have never been a fan of John Edwards, but it is time for the gov’t to focus on more important things,” Trumpwrote.

“This is a very, very tough trial, to start off with. And a lot of people are saying it’s not a trial that the government’s going to win,” Trump added on Fox News. “I really think we have better things to do. … And frankly, a lot of people say, and a lot of very good lawyers have told me, that the government doesn’t have a good case. They’re spending months and years on this case.”

The jury in the Edwards case ultimately acquitted him on one count and deadlocked on five others. The government elected not to retry him and dismissed the charges.

“Trump tweeted about John Edwards’ culpability, so he was certainly aware of the problem of paying off mistresses” during a campaign, said Rick Hasen a University of California law professor. “If Cohen’s story is corroborated and is believed, the most likely conclusion is that Trump did this knowing he was violating the law.”

If there’s no direct or strong proof that Cohen told Trump the payments were illegal, Trump could also have another defense: that it was reasonable to assume that his lawyer was making arrangements that were legal.

“One way to show you didn’t willfully or knowingly break the law, you assume, would be to say you relied on your lawyer,” said Grewal, the University of Iowa law professor. “If you’re just bumbling around and telling your lawyer to do things, you would imagine your lawyer taking care of those things would not break the law.”

Trump indicated in another tweet Wednesday that Cohen’s legal advice had not always been first rate. “If anyone is looking for a good lawyer, I would strongly suggest that you don’t retain the services of Michael Cohen!” the presidentwrote.

Similar issues of intent have already arisen in a couple of cases stemming from special counsel Robert Mueller’s investigation into possible collusion between the Trump campaign and Russia.

A Russian company indicted in a case that Mueller brought in February over Russian internet trolls’ effort to foment discord during the 2016 election, primarily by backing Trump, has argued that the conspiracy charge against it is legally defective because prosecutors never told the grand jury that the company had to know its conduct was illegal in order to be guilty.

Prosecutors say the nature of the broad conspiracy charge in that case means no such intent must be shown. A federal judge has not yet ruled on the issue.

At the just-completed trial of former Paul Manafort, Trump’s former campaign chairman, prosecutors and defense attorneys also squared off over whether Manafort intentionally violated the law by filing false tax returns and by failing to file reports on foreign bank accounts. The jury convicted Manafort on the tax charges and one of four charges relating to unreported accounts.

One potentially significant twist with Trump is that Justice Department policy says he can’t be indicted while in office. So the question may never directly arise about whether to file a charge against him. Instead, the issue may be whether to include the alleged campaign finance offenses in a report to Congress that could lead to impeachment.

Even there, however, the intent issue could loom large because the Justice Department is likely to take into account how it would have handled a potential criminal case against Trump.

“If Mueller writes a report on potential crimes by the president, there has to be some indication of how serious this is and what does it mean in terms of whether he would have been charged with a crime, even if DOJ is not going to have an indictment of the president,” said Hasen, the University of California law professor. “There’s a lot of ways further analysis of Trump’s motives could come, aside from actually charging him with a crime.”